The saves are stored in your browser’s cookies. To keep your saves, you need to make sure your browser allows cookies on itch.io and doesn’t erase them over time.
Unfortunately some mobile devices delete those cookies regardless of your settings. I’ve not found any work around that.
If you can play on laptop/desktop, it would be ideal.
I’m hoping it’ll be possible to add a save to file option, but I can’t guarantee it’ll happen as of now. And even if I’m able to add that feature, the save files will be obsolete after each content update.